Please note:
1) for the plastic wrap, if it is still usable, wrap again the tub and use generously wide tape to seal the openings
If the wrap is badly damaged, you should get some new one from a home center. Close with tape.
2) For the hammer marks: I will need to see the pictures.
Wood swells when it is wet and there is the possibility that it slightly returns back if you blot it with a wet cloth (not just dump, make it dripping wet) or by pouring water on it for at least 1 hour.
If the wood is not returning, you can apply the dump cloth on the damaged area and press it with an iron (cotton-high temperature, apply intermittently for few seconds).
A third option is to sand it. The wood is not treated (excepted for for the bottom plank head). I think you should be able to sand only the faces which are damaged and not the whole top.
The corner fillet (mentori) should be made with a hand plane but this tool is difficult to use. You may employ a sander but be aware that the corner will become roundish instead.
COMMENTS~